152 



The cross section areas, X, at the tidal stations at which discharges 

 and velocities are to be computed, similarly m,ay be read from a 

 diagram, constructed by taking off with a planimeter the area of the cross 

 section at high and low water, and at intermediate elevations if necessary. 



309. Form for computations. — The computations proceed from the 

 head oi tide downstream. A convenient form, developed for the 

 cubature of the Delaware River, is shown in figure 48. To briefly 

 illustrate the process, the computations for six half-hourly intervals 

 only in the first two reaches below the head of tide and in the lowest 

 reach, are entered on the same sheet. In the actual computation a 

 separate sheet is used for each successive reach between the tide 

 stations. The computation shown for the first reach is abl)reviated 

 as explained in paragraph 310. 



The times and the heights of the tides at the upper and lower sta- 

 tions, selected for the cubature as explained in paragraphs 303 to 306 

 are entered in columns (1), (2), and (3), and the mean of columns (2) 

 and (3) is entered in column (4). Column (5) designates the interval 

 to which the entries in the succeeding columns apply. Column (6) 

 is the mean of the given and preceding entries in column (4) and is 

 therefore the mean elevation, during the interval, of the mean tides in 

 the section. Column (7) is the surface area in the reach at the eleva- 

 tion shown in column (6). Column (8) is the algebraic increase in 

 the entries in column (4) during the interval. The product of columns 

 (7) and (8) is the value of AF for the interval (equation 185) ; entered in 

 column (9). The increases, during the interval, in the tidal volumes 

 of any separately cubatured tidal tributaries which enter the reach are 

 inserted in columns (10) and (11). The total tidal volume, column 

 (12), is the sum of columns (9) to (11). The total increase in volume 

 during the interval in the upstream reaches, as previously computed 

 for these reaches, is entered in column (13). The addition of the 

 increase in the reach, column (12), gives the total increase, SAF, at 

 the lower station (column 14). The division by A^= 1,800 seconds, 

 gives the mean discharge during the period, column (15), and the 

 addition of the fresh-water inflow (with the negative sign) give the 

 total discharge, column (16). The mean elevation of the tide at the 

 lower station, column (17), is the mean of the given and preceding 

 entries in column (3). The corresponding area of the cross section at 

 this station is entered in column (18); and the mean current velocity 

 during the interval, column (19), obtained by dividing the entries in 

 column (16) by those in column (18). 



310. Because of the steady increase in the width of nearly all natural 

 tidal channels from the head of tide to the entrance, the increases in 

 the tidal volume between the stations near the head of the estuary are 

 relatively very small. The upstream station may therefore be placed 

 below the head of tide, and the successive values of AT^ at tliis 



